A dominating question in the public evaluation of the COVID-19 situation during the 2020 pandemic is the estimation of the basic reproduction number \(R_0\) , the number of new infections which are caused (on average) from a single infected individual. While this number is prominently discussed in the news about COVID-19, it is an important variable for disease transmission in general ([1]}, [2]}). In order to estimate the reproduction number of a disease the so-called generation time \(G\)  plays an important role (see Euler-Lotka-Equation e.g. in [3]}). The generation time \(G\)  is defined as the time difference between the infection time of a randomly chosen infected individual and his or her infector. Let \(\varphi _G\)  denote the density of the generation time \(G\) . Then \(R_0^{-1}=F_R(G)\) , where (this is the Euler-Lotka-Equation, see e.g. [3]}, [1]})
\(F_R(G):=\int _0^{\infty }e^{-rt}\varphi _G(t)dt\) 
